# Properties

 Label 280.2.ba Level $280$ Weight $2$ Character orbit 280.ba Rep. character $\chi_{280}(19,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $88$ Newform subspaces $2$ Sturm bound $96$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$280 = 2^{3} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 280.ba (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$280$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$96$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(280, [\chi])$$.

Total New Old
Modular forms 104 104 0
Cusp forms 88 88 0
Eisenstein series 16 16 0

## Trace form

 $$88 q - 2 q^{4} - 40 q^{9} + O(q^{10})$$ $$88 q - 2 q^{4} - 40 q^{9} - 12 q^{10} - 4 q^{11} - 14 q^{14} - 6 q^{16} - 12 q^{19} + 12 q^{24} - 2 q^{25} + 6 q^{26} - 20 q^{30} - 2 q^{35} - 20 q^{36} + 12 q^{40} + 30 q^{44} + 38 q^{46} - 8 q^{49} - 40 q^{50} + 20 q^{51} + 60 q^{54} - 72 q^{56} - 60 q^{59} - 42 q^{60} + 4 q^{64} + 8 q^{65} + 84 q^{66} - 22 q^{70} + 2 q^{74} - 6 q^{75} - 96 q^{80} - 36 q^{81} - 100 q^{84} - 8 q^{86} - 36 q^{89} + 32 q^{91} - 42 q^{94} + 96 q^{96} + 80 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(280, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
280.2.ba.a $8$ $2.236$ 8.0.3317760000.3 $$\Q(\sqrt{-10})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{4}q^{2}-2\beta _{3}q^{4}+\beta _{6}q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$$
280.2.ba.b $80$ $2.236$ None $$0$$ $$0$$ $$0$$ $$0$$